Highly efficient superconducting diode effect in unconventional $p$-wave magnets

We investigate the emergence of superconducting phases, both with zero and finite Cooper-pair center of mass momenta, in recently proposed unconventional $p$-wave magnets. As a consequence, we find that, while these magnetic phases are in principle compatible with a conventional pairing state at zero field, a Fulde-Ferrell phase can generally be promoted as the leading instability under the application of a finite magnetic field. Interestingly, by calculating the efficiency of the superconducting diode effect of this finite momentum pairing state via a Ginzburg-Landau theory, we uncover that a high efficiency can be obtained in these systems for experimentally relevant spin splittings. Therefore, our prediction reveals that the experimental discovery of these new materials represents a promising platform for the construction of energy-efficient logic circuits that can potentially be used, e.g., in the fields of classical and quantum computing.